tanx = 6, so we take inverse tangent of 6 and get 1.405647... If we divide by pi, the value is about .4474pi. With tangent, the second angle where this works is pi away, which means
x = 0.4474pi and 1.4474pi
b) sinx - ½tanx = 0
Rewriting, we get
sinx - ½sinx/cosx = 0
Factoring out sine we get
sinx(1 - ½*1/cosx) = 0
This means either sinx = 0 or
1 = ½*1/cosx, which solves to
½ = cosx
Sine is 0 at 0, pi and 2pi. Cosine is ½ at pi/3 and 2pi/3
c) cos²x = ½
Take square roots of both sides and we get
cosx = +/- sqrt(2)/2
This is true at four "famous" angles, pi/4, 3pi/4, 5pi/4 and 7pi/4.
a) tanx - 6 = 0
ReplyDeleteThis is the same as
tanx = 6, so we take inverse tangent of 6 and get 1.405647... If we divide by pi, the value is about .4474pi. With tangent, the second angle where this works is pi away, which means
x = 0.4474pi and 1.4474pi
b) sinx - ½tanx = 0
Rewriting, we get
sinx - ½sinx/cosx = 0
Factoring out sine we get
sinx(1 - ½*1/cosx) = 0
This means either sinx = 0 or
1 = ½*1/cosx, which solves to
½ = cosx
Sine is 0 at 0, pi and 2pi. Cosine is ½ at pi/3 and 2pi/3
c) cos²x = ½
Take square roots of both sides and we get
cosx = +/- sqrt(2)/2
This is true at four "famous" angles,
pi/4, 3pi/4, 5pi/4 and 7pi/4.